The Von Staudt-Clausen theorem has two parts: generating denominators of the B_2n and the actual values. Both operations can be demonstrated in triangles A143343 and A080092 by following the procedures outlined in [Wikipedia - Bernoulli numbers] and summarized in A143343.

Extract primes from even numbered rows of triangle A143343 but also include "2" as row 1. The rows are thus 1, 2, 4, 6, ..., generating denominators of B_1, B_2, B_4, ..., as well as B_1, B_2, B_4, ..., as two parts of the Von Staudt-Clausen theorem.

The second operation is the Von Staudt-Clausen representation of Bn, obtained by starting with "1" then subtracting the reciprocals of terms in each row. (Cf. A143343 for a detailed explanation of the operations.) (End)